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244     ON  THE COMPOSITION  AND  RESOLUTION  OF  STREAMS  OF
that the light enters the medium at the first surface, and leaves it at the second, in a direction normal to the surface, or very nearly so, and likewise that the refracting power of the medium for the two pencils is not very different, so that the effect of reflexion at the two surfaces may be disregarded, the only sensible effect being to diminish the intensity of each of the two pencils in the same proportion, without affecting its state of polarization. These views would lead us to scrutinize very carefully any experimental evidence brought forward which would lead to the conclusion, that the two polarized pencils which a doubly refracting medium was capable of propagating in a given direction were polarized otherwise than oppositely.
7.    In ordinary doubly refracting crystals, whether uniaxal or biaxal, and in doubly refracting liquids, such as syrop of sugar, it is generally admitted that the two pencils transmitted in a given direction are oppositely polarized.    In the former case the two  pencils  are  polarized  in  rectangular  planes, in the  latter they are  circularly polarized, one  being right-handed and the other left-handed.    The same is the case with quartz for pencils transmitted in the direction of the axis; but in following out the researches in which he so successfully connected the phenomena, identical with those of a doubly refracting liquid, which quartz exhibits in the direction of the axis, with the phenomena which it exhibits as a uniaxal crystal, Mr Airy met with an experimental result which seemed to shew that while the ellipses which characterize the two streams transmitted in a given direction, oblique to the axis, have their major axes situated, one in a principal plane, and the other perpendicular to the principal plane, arid  the directions of revolution are opposite, the eccentricities  of the  ellipses,  though  nearly, are   not   quite  equal*. This conclusion depended upon the result of certain experiments made by means of a Fresnel's rhomb.    The nature of the experiments  seemed  to  eliminate  the  effect of an   error in  the rhomb, that is, a deviation from 90 in the retardation of phase which it produced in a pencil polarized in the plane of reflexion relatively to a pencil polarized in a plane perpendicular to the former.    The  effect of a possible  index  error in the plane of reflexion seemed also to be eliminated; and the quantities on
* Cambridge Philosophical Transactions, Vol. iv. p. 204.